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%I #6 Aug 28 2019 08:16:05
%S 0,0,1,1,2,1,4,1,7,3,16,1,49,1,129,17,415,1,1408,1,4659,130,16081,1,
%T 56858,15,200171,1367,716733,1,2590529,1,9393119,16082,34319668,142,
%U 126104312,1,465076161,200172,1723097474,1,6408573532,1,23910271229,2587214,89493903439
%N Number of imprimitive (periodic) 2n-bead black-white complementable necklaces with n black beads.
%C a(p)=1 for prime p.
%F a(n)=A045629(n) - A045632(n).
%t A045629[n_] := If[n==0, 1, (1/(2n)) DivisorSum[n, EulerPhi[n/#] Binomial[ 2 # - 1, # - 1] + EulerPhi[2 (n/#)] 2^(# - 1)&]];
%t A045632[n_] := If[n==0, 1, Sum[MoebiusMu[n/d] A045629[d], {d, Divisors[n]}]];
%t a[n_] := A045629[n] - A045632[n];
%t Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Aug 28 2019 *)
%K easy,nonn
%O 0,5
%A _Valery A. Liskovets_, Jan 17 2006
%E More terms from _Jean-François Alcover_, Aug 28 2019
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